A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

Abstract

A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent network. Training samples entail global pressure and saturation maps, at a series of time steps, generated by simulating oil-water flow in many (1500 in our case) realizations of a 2D channelized system. After training, the 'recurrent R-U-Net' surrogate model is shown to be capable of accurately predicting dynamic pressure and saturation maps and well rates (e.g., time-varying oil and water rates at production wells) for new geological realizations. Assessments demonstrating high surrogatemodel accuracy are presented for an individual geological realization and for an ensemble of 500 test geomodels. The surrogate model is then used for the challenging problem of data assimilation (history matching) in a channelized system. For this study, posterior reservoir models are generated using the randomized maximum likelihood method, with the permeability field represented using the recently developed CNN-PCA parameterization. The flow responses required during the data assimilation procedure are provided by the recurrent R-U-Net. The overall approach is shown to lead to substantial reduction in prediction uncertainty. High-fidelity numerical simulation results for the posterior geomodels (generated by the surrogate-based data assimilation procedure) are shown to be in essential agreement with the recurrent R-U-Net predictions. The accuracy and dramatic speedup provided by 1 arXiv:1908.05823v1 [cs.LG] 16 Aug 2019 the surrogate model suggest that it may eventually enable the application of more formal posterior sampling methods in realistic problems. our case), this surrogate model can provide flow predictions in close agreement with the underlying flow simulator, but with a significant reduction in computational cost. Thus this approach enables the application of accurate but computationally demanding inverse modeling procedures.There has been extensive research on constructing surrogate models for subsurface flow prediction. These can be generally classified, based on the mathematical formulation, into physics-based and data-driven procedures (though these categories are not mutually exclusive). The physics-based methods typically neglect or simplify physical or numerical aspects of the problem, through, for example, reduced-physics modeling, coarse-grid modeling, or proper orthogonal decomposition (POD) based reduced-order modeling (ROM). A variety of POD-based ROMs, in which the state variables and the system of equations are projected into low-dimensional space and then solved, have been applied for a range of subsurface flow problems [1, 2, 3, 4, 5]. These ROMs can be effective, although they are generally only accurate when new (test) runs are sufficiently 'close' to training runs. In addition, the applicat...

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